# Electric Field due to Point Charges

## Homework Statement

[/B]

The following is on a practice exam I have been completing. In advance, it is part b I am struggling with.

Two point charges Q1 = +5*10^(-6)C and -2*10^(-6)C are 50cm apart.
a) Where along a line that passes through the two charges is the electric potential zero (apart
from at r=infinity)?

b) Determine the magnitude of the electric field at that point. Explain why the electric field is non-zero.

E=kQ/r^2

V=kQ/r

E=dV/dr

## The Attempt at a Solution

I got part A immediately using V=kQ/r and superposition of electric potential, finding it to be 0.36m (which matched the solution). It is part b that I am struggling with. I have as follows:

E=kQ/r^2
Using superposition of electric fields, this gives
E = k(5/(0.36^2) + -2/(0.5-0.36)^2), where k=1/(4*pi*E_0). This gave me an electric field of -570367N/C; however, the solution said it was 1.2*10^6 N/C. I believe the issue was in my implementation of the -2C in the above equation; however, am not entirely sure why this is incorrect or what to do to fix it.

As for the explanation, my belief is that because E is changing in potential with respective to distance, as long as the potential is not set at a constant 0 - that is, the potential is changing as distance changes - the electric field could be non-zero. I think I'm okay with this, but please do not hesitate to correct me if I'm wrong!

I'd really appreciate some help in figuring this out - or even just in where I went wrong. Please let me know if I've forgotten anything or my working isn't clear.

Thank you so much